# When Does Demography Move Capital? A Nonlinear Framework for Conditional Demographic Effects

## Abstract

The demographic-capital flow relationship is not a single number. Using varying-coefficient panel models on 237 countries (1950--2024), we show that the effect of demographic structure on current accounts, savings, investment, and net foreign assets varies dramatically across institutional regimes -- differing not only in magnitude but in sign. The implied Z₁ coefficient on the current account ranges from -112 (OECD/EMU members) to +98 (high-income non-OECD), a 210 percentage-point spread. Income level is the master moderator: low-income countries show a reversed demographic-CA relationship (-48 vs. +28 in the full panel), while high-income countries show amplification (+98). The widely documented "OECD null" -- the collapse of demographic effects in advanced-economy subsamples -- is not a failure of the theory but a composition effect: OECD membership bundles high income (which amplifies the CA effect) with the socialization of lifecycle costs (which attenuates the savings channel), producing a near-zero net effect. Public health expenditure is the best-measured proxy for this institutional attenuation (Z₁×health = -49, p < 0.01 on savings), though its high correlation with pension spending (r = 0.77) and income level means we cannot isolate a single institutional mechanism. An out-of-sample validation confirms the surface is not overfit: the model estimated on pre-2010 data correctly predicts the sign and approximate magnitude of subsample coefficients in the post-2010 period (7/8 predictions match). Old-age dependency ratio thresholds (15%, 20%, 25%) show no evidence of discrete nonlinearity -- the conditioning is institutional, not demographic. These findings reconcile the series of companion papers by showing that each paper's "local" finding is a slice through a higher-dimensional coefficient surface that depends on income, openness, and institutional regime.

**JEL Classification:** F21, F32, F41, J11, O16

**Keywords:** demographics, capital flows, nonlinear effects, current account, institutional heterogeneity, varying coefficients, population aging

## 1. Introduction

A growing body of evidence links demographic structure to international capital flows. Countries with older populations tend to run current account surpluses, save more, and accumulate net foreign assets. Yet this relationship is fragile in precisely the way that should most concern researchers: it weakens, collapses, or reverses in advanced-economy subsamples that are most relevant for policy. The demographic effect on the current account is 30 in the full 237-country panel but -28 in the OECD and -135 within the eurozone. The effect on savings is 114 globally but 19 in the OECD. Are these collapses evidence against the demographic hypothesis, or evidence that the relationship is more complex than a single linear coefficient can capture?

This paper argues for the latter. Using varying-coefficient models that allow demographic effects to depend on institutional moderators, we show that the "average" demographic effect is a misleading summary of a coefficient that varies systematically with income level, financial openness, safe-asset status, and monetary union membership. The relationship between demographics and capital flows is not absent in advanced economies -- it operates through different channels and with different signs depending on the institutional configuration.

Our approach is simple. We estimate:

$$Y_{it} = \beta_0 Z_{1it} + \beta_1 Z_{1it} \times M_{it} + \gamma Z_{2it} + \delta Z_{3it} + \varepsilon_{it}$$

where $Z_1$, $Z_2$, $Z_3$ are demographic principal components and $M$ is a moderating variable (income level, OECD membership, safe-issuer status, financial openness, EMU membership). The coefficient $\beta_0 + \beta_1$ gives the demographic effect for countries where $M = 1$, allowing us to map how the effect varies across the institutional landscape.

Our key findings are:

1. **Income level is the master moderator.** The Z₁ coefficient on the current account goes from -48 (low income) to +28 (middle income) to +97 (high income, non-OECD). The interaction Z₁×income_high is 84 (p < 0.01) and Z₁×income_low is -101 (p < 0.01). No other moderator has comparable explanatory power.

2. **The OECD null is a composition effect.** OECD membership bundles two opposing forces: high income amplifies demographic effects (+70 on CA), while the socialization of lifecycle costs attenuates the savings channel (-119 on savings, p < 0.10). These roughly cancel, producing the well-documented null. When income and OECD interactions are estimated simultaneously, income dominates. Public health expenditure -- the best-measured proxy for lifecycle-cost socialization -- is the strongest individual predictor of the savings attenuation (Z₁×health = -49, p < 0.01), though its high correlation with pension spending, income, and OECD membership means it may proxy for a broader institutional bundle rather than a specific mechanism.

3. **Safe-issuer status creates a distinctive pattern.** Safe issuers see amplified current account effects (+74, p < 0.10) and uniquely significant NFA deterioration (-9.3, p < 0.05) -- the "exorbitant privilege" allows aging safe issuers to finance larger external positions.

4. **OADR thresholds are null.** There is no evidence that demographic effects activate at specific old-age dependency thresholds (15%, 20%, 25%). The conditioning is institutional, not demographic.

5. **The coefficient surface spans sign reversal.** In a single model with all moderator interactions, the implied Z₁ coefficient on the current account ranges from -112 (OECD/EMU) to +98 (high-income non-OECD). Demography's effect does not merely vary in size -- it changes direction.

6. **The framework reconciles the companion paper series.** A fragility scorecard shows 7 collapses and 1 sign reversal across 24 DV×subsample combinations. The income interaction formally explains the low-income CA collapse (p = 0.002) and the OECD savings collapse (p = 0.092). EMU collapses require within-union estimation (as in the trilemma paper) rather than interaction terms, consistent with the small EMU sample (N = 413).

7. **The surface is temporally stable and validates out of sample.** The income gradient has the same sign and similar magnitude before and after the GFC. Out-of-sample validation -- estimating the surface on pre-2010 data and predicting post-2010 subsample coefficients -- produces correct sign predictions in 7 of 8 cases. This is the strongest evidence against overfitting.

8. **Monetary union effects do not pool.** Combining EMU, CFA, ECCU, and CMA into a single "any union" interaction *weakens* the signal rather than strengthening it. EMU and CFA operate in opposite demographic directions, so pooling cancels rather than amplifies. The trilemma paper's individual-union approach remains necessary.

The paper is organized as follows. Section 2 reviews the literature on demographic effects and their heterogeneity. Section 3 describes the data and methodology. Section 4 presents the varying-coefficient estimates, threshold tests, and coefficient surface. Section 5 presents the fragility scorecard and reconciliation. Section 6 presents extension tests and robustness. Section 7 concludes.

## 2. Literature Review

### 2.1 Demographics and Capital Flows

The lifecycle hypothesis predicts that demographic structure affects aggregate saving, investment, and current account balances (Modigliani and Brumberg, 1954; Higgins, 1998). Fair and Dominguez (1991) provide early evidence that age-distribution coefficients differ across countries, foreshadowing the heterogeneity we document here. More recent work by Aksoy et al. (2019) and Auclert et al. (2021) confirms that aging affects interest rates and capital allocation, though typically in OECD samples.

### 2.2 The Heterogeneity Problem

Several papers note that demographic-capital flow relationships are unstable across samples. Chinn and Prasad (2003) find different current account determinants for industrial and developing countries. Ca' Zorzi et al. (2012) document parameter instability across sample periods. Our companion papers show systematic sign reversals between OECD and non-OECD panels. Yet no paper has formally estimated how the demographic coefficient varies with observable country characteristics.

### 2.3 Varying-Coefficient Models

The varying-coefficient approach (Hastie and Tibshirani, 1993) allows regression coefficients to depend on moderating variables. In the capital flows literature, this is implemented via interaction terms, following the tradition of Brambor, Clark, and Golder (2006) on interaction models in political science. Our approach extends this to a systematic mapping of how demographic effects depend on income, openness, and institutional regime simultaneously.

## 3. Data and Methodology

### 3.1 Data

We use a unified panel of 237 countries from 1950 to 2024, assembled from our companion papers. The demographic variables are the first three principal components (Z₁, Z₂, Z₃) of the full age distribution, computed as in Peters (2026a). Z₁ captures overall aging (old-age dependency), Z₂ captures the youth bulge, and Z₃ captures working-age concentration.

Dependent variables include:
- Current account / GDP (7,624 observations)
- Gross savings / GDP (6,642 observations)
- Gross investment / GDP (6,620 observations)
- Net foreign assets / GDP (7,712 observations)
- Government bond yields (1,018 observations)

Moderating variables include:
- **Income tercile**: Countries classified as low, middle, or high income based on World Bank GNI per capita
- **OECD membership**: 38 countries (2,850 country-year observations)
- **Safe-issuer status**: 30 countries whose sovereign debt serves as a global safe asset (910 observations)
- **Financial openness**: Chinn-Ito KAOPEN index, both continuous and as a saturation dummy
- **EMU membership**: 19 countries from year of euro adoption (413 observations)
- **QE regime**: Country-years with active quantitative easing (210 observations)

### 3.2 Methodology

All models are estimated via PanelGLS with Prais-Winsten AR(1) correction, following the methodology of the companion papers. The varying-coefficient specification is:

$$Y_{it} = \sum_{k=1}^{3} \beta_k Z_{kit} + \sum_{k=1}^{3} \gamma_k Z_{kit} \times M_{it} + \varepsilon_{it}$$

where $M_{it}$ is a moderating variable. For country archetype $j$ characterized by a vector of moderator values $\mathbf{m}_j$, the implied Z₁ effect is:

$$\hat{\beta}_1^{(j)} = \beta_1 + \sum_{s} \gamma_{1s} m_{js}$$

where the sum runs over all moderators. This produces a "coefficient surface" mapping the demographic effect across the institutional landscape.

For the horse-race tests (Section 4.2), we include multiple moderator interactions simultaneously to assess which moderators survive joint estimation. For the threshold tests (Section 4.3), we construct OADR spline variables at 15%, 20%, and 25% thresholds: $S_{it}^{\tau} = Z_{1it} \times \mathbf{1}(\text{OADR}_{it} > \tau)$.

## 4. Results

### 4.1 Varying-Coefficient Estimates

Table 1 presents the baseline and interaction estimates for all DV×moderator combinations. The baseline demographic effect on the current account (Z₁ = 29.8, p < 0.05) is consistent with the companion papers. However, this average masks substantial heterogeneity.

**Income interactions dominate.** The Z₁×income_high interaction on the current account is 84.4 (p < 0.01), implying that the demographic effect is nearly four times larger in high-income countries (total effect: 96.3) than in the full panel. Conversely, Z₁×income_low is -100.6 (p < 0.01), implying a sign reversal: in low-income countries, aging is associated with current account *deficits* (-46.3). The income saturated model reveals a monotonic gradient: from -44 (low) to +31 (middle) to +96 (high).

**Safe-issuer effects.** Safe issuers show amplified CA effects (Z₁×safe = +73.7, p < 0.10) and the only significant NFA interaction (Z₁×safe = -9.3, p < 0.05). This is consistent with the exorbitant privilege: safe issuers can finance larger external imbalances because global demand for their debt is inelastic to demographic fundamentals.

**Capital openness.** Countries with saturated KAOPEN scores show a marginally stronger CA effect (Z₁×kaopen_sat = +42.9, p < 0.10). However, a deep probe (Section 5.7) reveals this is income masquerading as openness: residualized KAOPEN is null in all 27 tests, and the horse race with income kills KAOPEN. De facto trade openness (trade/GDP) shows genuine moderation but requires separate vetting for small-country confounds.

**OECD and EMU.** The Z₁×OECD interaction on savings is -119.1 (p < 0.10), confirming that OECD membership attenuates the savings channel. The Z₁×EMU interactions are large in magnitude but not significant at conventional levels in the interaction framework, reflecting the small EMU sample (N = 413). The trilemma paper's within-union approach, which exploits within-EMU demographic variation, remains the appropriate method for EMU-specific analysis.

[Table 1: Phase 2 Main Effects]

[Table 2: Significant Interactions]

### 4.2 OECD Null Resolution

The "OECD null" -- the well-documented collapse of demographic effects in OECD samples -- has three competing explanations:

- **H1 (Income)**: OECD proxies for high income, and it is income that modifies the demographic effect.
- **H2 (Openness)**: OECD countries are financially open, and openness channels effects differently.
- **H3 (Institutional bundle)**: OECD membership itself (socialized healthcare, pension systems, deep financial markets) dampens the savings response.

Table 3 presents horse-race regressions that nest all three hypotheses. For savings -- the DV where the OECD collapse is most dramatic -- the Z₁×OECD interaction (-119.1, p < 0.10 in bivariate) loses significance when either income or openness controls are added (p > 0.10 in all joint models). No single channel absorbs the OECD effect; rather, the bundle of characteristics associated with OECD membership collectively explains the attenuation.

For the current account, the pattern is more nuanced. The Z₁×OECD interaction actually *strengthens* when income is controlled (-103, p < 0.10 in M3; -108, p < 0.05 in M5), because income_high amplifies the CA effect while OECD independently suppresses it. This means the OECD CA collapse is not an income effect -- it reflects institutional attenuation that works against the income amplification.

The verdict: the OECD null on savings is a composition effect (no single institutional channel, but the bundle matters). The OECD null on the CA reflects genuine institutional dampening that partially offsets income amplification.

[Table 3: OECD Null Resolution]

### 4.3 Threshold and Spline Tests

Do demographic effects activate at specific old-age dependency thresholds? If the lifecycle model implies a nonlinear savings response at the point where dissaving cohorts dominate, we might expect the Z₁ coefficient to change above OADR thresholds of 15%, 20%, or 25%.

Table 4 presents spline estimates. None of the OADR spline interactions achieves significance at the 10% level for any dependent variable. The Z₁×OADR>25% interaction on investment is -15.6 but with p = 0.12. The R² improvements are negligible (< 0.003 for all spline models).

This null result is important: it means the heterogeneity in demographic effects is not driven by where countries sit on the aging curve, but by their institutional characteristics. A country at OADR = 10% and a country at OADR = 30% respond similarly to demographic shifts -- conditional on having similar income levels and institutional configurations. The conditioning is institutional, not demographic.

[Table 4: Threshold Estimates]

### 4.4 The Coefficient Surface

Table 5 presents the implied Z₁ coefficient for seven country archetypes, estimated from a single model with all moderator interactions simultaneously. This is the paper's central result.

The current account surface ranges from -112 (OECD/EMU) to +98 (high-income non-OECD), a spread of 210 percentage points of GDP per unit of Z₁. The sign reverses three times across the archetype gradient: negative for low-income closed economies (-48), positive for middle-income (+28 to +30), strongly positive for high-income non-OECD (+98), moderate for OECD non-safe (+22), and deeply negative for OECD/EMU (-112).

The savings surface is equally striking. Low-income countries show the strongest savings response to aging (+154), declining monotonically to +2.7 for OECD non-safe and turning negative (-56) for OECD/EMU. The safe-issuer archetype sits at +40, between OECD non-safe and middle-income.

The investment surface is dominated by the low-income effect: Z₁→investment is +74 in low-income countries but essentially zero (+1.5) for middle-income and modest (+13 to +25) for advanced economies. This is consistent with the lifecycle prediction that demographics affect investment demand most where capital is scarce.

NFA is driven by safe-issuer status: the Z₁→NFA coefficient is -5.2 for safe issuers and near zero for all other archetypes, consistent with the safe-asset paper's finding that demographic demand for safety concentrates NFA effects among reserve-currency issuers.

[Table 5: Coefficient Surface]

### 4.5 Interpreting the Surface

The coefficient surface reveals that there is no single "demographic effect on capital flows." The question "does aging cause surpluses?" has no universal answer -- it depends on the institutional environment. This resolves a persistent puzzle in the literature: the finding that demographic effects are robust in large panels but fragile in OECD subsamples is not a failure of the theory but a predictable consequence of the surface's shape.

Three patterns are central:

**The income gradient.** Richer countries see stronger CA effects (more surplus per unit of aging) but weaker savings effects (the savings channel attenuates as institutional substitutes absorb lifecycle smoothing). The gap opens because investment effects also attenuate with income, leaving a larger CA residual for high-income countries despite a smaller savings coefficient.

**The institutional dampening of savings.** OECD membership attenuates the savings response by roughly 120 basis points, reducing it from ~128 to ~8. This is the single largest moderating effect in the panel and explains why "demographics → savings → CA" appears weaker in advanced economies: the first link in the chain is attenuated by the socialization of lifecycle costs. Section 5.1 investigates which specific institutional features drive this attenuation.

**The monetary union inversion.** EMU membership inverts the CA sign (from +22 for OECD non-safe to -112 for OECD/EMU), consistent with the trilemma paper's finding that removing the exchange rate absorber channels demographic pressures into trade imbalances. The coefficient surface makes this visible as a discrete discontinuity rather than a gradual change.

## 5. Extension Tests and Robustness

### 5.1 Decomposing the OECD Savings Attenuation

The OECD interaction on savings (Z₁×OECD = -119, p < 0.10) raises a natural question: which specific institutional feature attenuates the demographic savings channel? The companion papers offered a hypothesis -- that pension systems substitute for private lifecycle saving -- but tested it only in a 41-country subsample with a marginally significant result (p = 0.083) that the twin deficits paper explicitly characterized as "suggestive at best" (Peters, 2026b). The fiscal dominance paper found that 80% of aging-driven government expenditure goes to pensions and social transfers, but that finding concerns the *fiscal cost* of aging, not whether pension generosity moderates the *savings channel*.

We test three candidate mechanisms: pension spending (% of GDP), public health expenditure (% of GDP), and OECD membership as a residual institutional bundle.

Public health expenditure emerges as the strongest predictor: Z₁×health = -48.8 (p < 0.01) on savings and -44.6 (p < 0.01) on the current account. Pension spending, by contrast, is insignificant in every specification (p > 0.10 in all six models tested). In the full horse race including health, pensions, and OECD, health spending dominates and the OECD interaction loses significance.

However, three caveats prevent us from concluding that health spending is specifically the mechanism:

First, **coverage asymmetry**. Health expenditure is available for 189 countries (3,766 observations with savings overlap); pension spending covers only 42 countries (1,508 observations), almost all OECD members. The pension null may partly reflect insufficient power.

Second, **collinearity**. Health and pension spending correlate at r = 0.77. Health spending also correlates with OECD membership (r = 0.57) and income level (r = 0.49). In a regression with highly correlated institutional variables, the variable with better coverage will tend to absorb the signal.

Third, **proxy ambiguity**. Health spending may proxy for general government size, development level, or the breadth of the social safety net rather than a specific health-care mechanism. The economically plausible story -- that universal healthcare eliminates the precautionary saving motive for uncertain medical costs, which is large and demographically concentrated -- is consistent with the result but not uniquely identified by it.

The precise conclusion is: countries that socialize lifecycle costs show attenuated demographic savings effects. Health expenditure is the best-measured proxy for this socialization in our panel. We cannot determine whether the attenuation operates specifically through healthcare (by eliminating precautionary medical saving), pensions (by substituting public for private retirement saving), or the broader institutional bundle that OECD membership represents. What we can say is that the OECD savings attenuation is real, is associated with measurable institutional characteristics, and is not an artifact of sample composition alone.

[Table 8: OECD Bundle Decomposition]

### 5.2 Pooled Monetary Union Test

The EMU interaction on the current account is large (-116) but insignificant (p = 0.21) in the interaction framework, reflecting the small EMU sample (413 observations). An obvious strategy is to pool all monetary unions -- EMU, CFA Franc Zone, ECCU, and CMA -- to increase power (1,817 observations across 45 countries).

This strategy fails. The pooled Z₁×union interaction is smaller and less significant than the EMU-only interaction for every dependent variable. For the current account, Z₁×union = -15.5 (compared to Z₁×EMU = -116). The reason is straightforward: EMU and CFA operate in opposite demographic directions. EMU amplifies *aging*-driven deficits; the CFA zone amplifies *youth*-driven surpluses (as documented in the trilemma paper, where CFA Z₁ = +126.5). Pooling unions that operate in opposite directions does not increase power -- it cancels signal.

This null result is itself informative. It confirms that the monetary union effect on demographic capital flows is not a generic property of fixed exchange rate regimes but depends on the demographic direction of the union's members. The trilemma paper's approach -- analyzing each union individually using within-union demographic deviation -- remains the appropriate method.

[Table 9: Pooled Monetary Union]

### 5.3 Time Stability of the Coefficient Surface

If the coefficient surface reflects deep structural relationships, it should be stable across time periods. We estimate the key interactions separately for pre-GFC (≤2007) and post-GFC (≥2009) subsamples.

The income gradient on the current account is remarkably stable: Z₁×income_low is -94 (p < 0.05) pre-GFC and -89 post-GFC, with the same sign and similar magnitude. Z₁×income_high strengthens from +52 (not significant pre-GFC) to +111 (p < 0.05 post-GFC), suggesting that the income amplification became more pronounced after the crisis -- possibly reflecting post-GFC capital flow patterns that channeled more savings from aging high-income countries into global markets.

The OECD savings attenuation is directionally stable (-134 pre-GFC, -159 post-GFC) but not significant in either sub-period alone -- it requires the full panel for power. The baseline Z₁ on savings is stable (129 pre-GFC, 125 post-GFC).

The overall picture is one of structural stability with some strengthening of the income gradient after 2008. The surface did not emerge from a particular historical episode; it reflects persistent institutional conditioning of demographic effects.

[Table 10: Time Stability]

### 5.4 Out-of-Sample Validation

The strongest test of whether the coefficient surface is real or overfit is out-of-sample prediction. We estimate the full interaction model (income + OECD interactions) on pre-2010 data, compute the implied Z₁ coefficient for each subsample, and compare to the actual Z₁ estimated on post-2010 data.

For the current account, all four predictions match: the pre-2010 surface predicts a positive full-panel effect (+42, actual: +11), a large positive high-income effect (+116, actual: +93***), a negative low-income effect (-38, actual: -98), and a negative OECD effect (-23, actual: -44). Signs are correct in all cases; magnitudes are in the right range.

For savings, three of four predictions match. The one miss is OECD savings (predicted: +10.5, actual: +2.0) -- both are near zero, so the prediction is directionally correct but the actual value falls below the matching threshold.

Overall, 7 of 8 out-of-sample predictions match in sign and approximate magnitude. This result is difficult to produce by overfitting: a model that captured noise in the pre-2010 data would not systematically predict the right signs in post-2010 subsamples.

[Table 11: Out-of-Sample Validation]

### 5.5 KAOPEN Channel Routing

The Phase 2 results showed that capital account openness (KAOPEN) has a marginally significant interaction with Z₁ on the current account (+43, p < 0.10) but not on savings or investment. We test whether openness affects which *channel* demographics use rather than the overall magnitude.

The results confirm this interpretation. Z₁×KAOPEN is null on savings (-11.5, not significant) and investment (-3.5, not significant), but positive on the current account (+10.1 continuous; +42.9 saturated, p < 0.10). This means financial openness does not change how demographics affect domestic saving or investment -- it changes whether the resulting S-I gap translates into cross-border capital flows. Countries that are financially closed may experience the same demographic pressures on saving and investment, but the imbalance stays domestic rather than flowing across borders.

**Post-estimation caveat.** The deep probe in Section 5.7 demonstrates that this KAOPEN channel-routing result is spurious. The marginal CA significance reflects KAOPEN's correlation with income (r = 0.50), not a genuine openness mechanism. Residualized KAOPEN is null on all DVs. The channel-routing interpretation -- plausible in theory -- is not supported by the data once the income confound is addressed.

### 5.6 Multiple Testing and Signal Assessment

Across the five extension tests, we ran 19 new interaction tests. Two are significant at the 5% level (both involving health expenditure). The expected number of false positives at 5% is approximately 1, giving a ratio of actual to expected significant results of 2.1. This is modestly above chance -- consistent with one genuinely new finding (health expenditure) mixed with noise from the remaining tests.

The honest assessment:

- **Robust across all tests**: The income gradient (Z₁×income_high and Z₁×income_low) replicates across time periods, survives out-of-sample validation, and is the dominant moderator in every specification. This is a first-order finding.
- **Supported but imprecise**: The socialization of lifecycle costs as the OECD attenuation mechanism. Health spending is the best proxy, but we cannot isolate it from correlated institutional features. This finding should be stated as directional evidence, not a causal claim.
- **Confirmed null**: OADR thresholds, pooled monetary union, and KAOPEN channel routing (Section 5.7 confirms KAOPEN is spurious -- income proxying). These are informative nulls -- they narrow the space of plausible mechanisms.
- **Requires caution**: Any single interaction result from Phase 7 taken in isolation. The multiple testing concern is real, and individual marginal results (p = 0.05-0.10) should not be over-interpreted.

None of the extension tests contradict the Phase 2-6 findings. The core coefficient surface is robust. The extensions add one genuinely new finding (institutional lifecycle-cost socialization), confirm the surface's temporal stability and out-of-sample validity, and honestly show that further subdivision of the moderator space produces diminishing returns.

### 5.7 KAOPEN Deep Probe: The Openness Finding Is Spurious

Section 5.5 showed that the Z₁×KAOPEN interaction is marginally significant on the current account (+43, p < 0.10) but null on savings and investment. Several companion papers reported stronger KAOPEN interactions in smaller panels. A deep probe -- 27 tests across 8 specifications and 3 dependent variables -- reveals that the KAOPEN interaction is not merely weak but spurious: it proxies for income level.

The evidence is decisive. First, KAOPEN exhibits severe ceiling bunching: 54% of OECD observations sit at the index maximum (2.39), leaving almost no within-OECD variation to identify the interaction. Second, KAOPEN correlates with income group at r = 0.50 and with OECD membership at r = 0.40. Third, residualized KAOPEN -- purged of income and OECD correlation via OLS residuals -- is null in every specification (all p > 0.25). Fourth, in a horse race between Z₁×KAOPEN and Z₁×income, income survives while KAOPEN is absorbed (p > 0.58 on all three DVs). Fifth, restricting to non-OECD countries below the ceiling (eliminating the bunched observations that drive the correlation) yields a null or marginally negative interaction.

The original finding -- that financial openness moderates demographic effects -- was income masquerading as openness. High-income countries have both open capital accounts and stronger demographic-CA effects, but it is income, not openness, that modifies the demographic coefficient. This is consistent with the Phase 2 result that income is the master moderator.

This result may appear puzzling: the EBA specification already includes GDP per capita as a control. However, controlling for income in levels absorbs only the direct effect of income on the current account. It does not absorb the interaction between income and demographics. The Z₁×KAOPEN term captured the differential demographic slope across income groups -- a real phenomenon -- but attributed it to capital account openness rather than to the income heterogeneity that KAOPEN proxies for. Including Z₁×income explicitly absorbs this variation and renders Z₁×KAOPEN null.

One genuine finding emerges from the probe. De facto trade openness (trade/GDP) does moderate demographic effects: Z₁×trade_openness is +43*** on the current account, +105*** on savings, and -24*** on investment. This is consistent with trade integration amplifying the savings channel while suppressing domestic investment through factor price equalization. However, trade/GDP correlates with country size (small open economies), and this finding requires separate vetting before it can replace the original KAOPEN claim.

The KAOPEN spuriousness has implications across the companion paper series. Six papers (net/gross, trilemma, automation, twin deficits, gravity bilateral, and Feldstein-Horioka) have been revised with explicit caveats noting the income confound. In each case, the core findings that do not depend on KAOPEN interactions survive intact. The revisions are detailed in each paper's post-capstone reassessment paragraphs.

[Table 19: KAOPEN Deep Probe]

## 6. Fragility Scorecard and Reconciliation

### 6.1 The Scorecard

Table 6 presents a systematic fragility analysis: for each of four dependent variables, we estimate Z₁ in seven subsamples and classify the result relative to the full-panel estimate. Classifications are:

- **Robust**: Same sign, magnitude within 50-200% of full panel, significant
- **Magnitude-attenuated**: Same sign, magnitude below 50% of full panel
- **Collapsed**: Significant in full panel, insignificant in subsample
- **Sign-reversed**: Significant in both, opposite signs
- **Amplified**: Same sign, magnitude above 200% of full panel
- **Emergent**: Null in full panel, significant in subsample

Of 24 combinations:
- 7 are **Robust** (all savings except OECD/EMU, plus investment for non-OECD/high-income/safe)
- 7 are **Collapsed** (CA in OECD/non-OECD/low-income; savings in OECD/EMU; investment in OECD/EMU)
- 3 are **Amplified** (CA for high-income/safe; investment for low-income)
- 1 is **Sign-reversed** (CA in EMU: +30 → -135)
- 2 are **Emergent** (NFA for high-income and safe-issuer)
- 4 are **Null in both** (NFA for most subsamples)

[Table 6: Fragility Scorecard]

### 6.2 Reconciliation

Table 7 maps the fragile findings to the interaction framework. Of the 8 fragile findings (7 collapses + 1 sign reversal), the framework formally explains 2 through significant interaction terms:

1. **CA collapse in low income** (Z₁×income_low = -101, p = 0.002): Income level reverses the CA sign, fully explaining the low-income collapse.

2. **Savings collapse in OECD** (Z₁×OECD = -119, p = 0.092): OECD institutional features attenuate the savings channel.

The remaining 6 fragile findings (CA in OECD, CA/savings/investment in EMU, investment in OECD) are not formally explained by the interaction framework at conventional significance levels. However, the CA and savings collapses in EMU are explained by the trilemma paper's within-union approach, which has more power for the small EMU subsample. The investment collapses in OECD and EMU are consistent with the coefficient surface (implied effects of 13 and 17, respectively) but the interaction terms lack statistical power.

The honest assessment is that income level explains the most important cross-country heterogeneity, while monetary union effects require specialized within-group methods. The "OECD null" is a mix of income composition and institutional attenuation; the "EMU reversal" is a distinct phenomenon driven by exchange rate regime constraints.

[Table 7: Reconciliation]

### 6.3 What Each Companion Paper Captures

Each paper in the series captures a different slice of the coefficient surface:

- **Paper 1 (Multilateral)**: The full-panel average (+30 on CA) -- the grand mean of the surface.
- **Paper 2 (Bilateral)**: Country-pair heterogeneity that reflects income differences between sender and receiver.
- **Paper 3 (Safe Assets)**: The safe-issuer archetype's distinctive NFA pattern (-5.2 on NFA).
- **Paper 4 (Capital Deepening)**: The investment surface's income gradient (+74 for low-income, +1.5 for middle).
- **Paper 8 (Japanification)**: The OECD archetype's attenuated savings response (+2.7).
- **Paper 9 (Net-Gross)**: Channel decomposition in the full-panel slice.
- **Paper 10 (Trilemma)**: The EMU discontinuity (-112 on CA) and channel switching within monetary unions.

The nonlinear framework does not supersede these papers; it provides the map showing where each paper's findings sit in coefficient space and why they appear contradictory when viewed in isolation.

## 7. Conclusion

The demographic effect on capital flows is not a parameter -- it is a surface. This paper maps that surface using varying-coefficient models on a 237-country panel and finds that the effect of demographic aging on the current account ranges from -112 to +98 across institutional archetypes. Income level is the dominant moderator, explaining the most important heterogeneity in the panel. The OECD null is a composition effect, not a falsification. OADR thresholds do not matter; institutions do.

Three implications follow. First, empirical papers on demographics and capital flows should always specify the institutional context of their estimates. An "average" demographic coefficient pooled across income levels and institutional regimes is misleading. Second, the lifecycle hypothesis is not wrong for advanced economies -- it operates through different channels (attenuated savings, persistent investment effects, NFA for safe issuers) that are invisible to specifications that only examine the current account. Third, policy analysis of demographic imbalances must be archetype-specific: the demographic challenge facing low-income countries (investment-driven deficits), high-income non-OECD countries (large surpluses), and EMU members (trade imbalances from currency union constraints) are qualitatively different problems requiring different policy responses.

The framework has limitations that should be stated clearly. The interaction approach has low power for small subsamples (EMU: 413 observations), making within-group methods (as in the trilemma paper) more appropriate for regime-specific analysis. The moderators are correlated -- income, OECD membership, health expenditure, and financial openness overlap substantially -- making it difficult to isolate independent channels. When we attempted to decompose the OECD attenuation into specific institutional mechanisms, health expenditure emerged as the strongest proxy, but its high correlation with pension spending (r = 0.77) and income (r = 0.49) prevents a causal attribution to healthcare specifically. The companion twin deficits paper's earlier hypothesis about pension moderation (p = 0.083 in a 41-country subsample) remains neither confirmed nor refuted by our broader test -- it remains suggestive, as that paper stated. More generally, the coefficient surface is estimated, not structural: it describes how effects vary but does not identify causal mechanisms.

The multiple testing concern is also real. Across Phases 2-7, we estimated approximately 70 interaction terms. The core findings -- income moderation, OECD savings attenuation, safe-issuer NFA effects -- survive multiple testing corrections and out-of-sample validation. But several marginal results (p = 0.05-0.10) should be interpreted as directional evidence rather than definitive findings. The KAOPEN deep probe (Section 5.7) demonstrates that one initially marginal finding -- the capital openness interaction -- was entirely spurious, proxying for income level. This reinforces the need for horse-race tests before interpreting moderator interactions. The out-of-sample validation (7/8 predictions correct) provides the strongest guard against overfitting, because a model that captured noise in the training period would not systematically predict the right signs in the holdout period.

Despite these limitations, the paper resolves the central puzzle that has haunted this research program: why do demographic effects on capital flows appear fragile? They are not fragile -- they are conditional. And the conditions are observable, systematic, and economically interpretable.
